Formula for the Gini Coefficient Using Areas A and B
The Gini coefficient can be calculated from a Lorenz curve diagram using the formula: . In this formula, Area A represents the area between the line of perfect equality and the Lorenz curve, while Area (A + B) represents the total area of the triangle under the line of perfect equality.
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Figure 2.4b: Gini Coefficients from Various Lorenz Curves
Imagine a standard diagram used to show income distribution, with cumulative population percentage on the horizontal axis and cumulative income percentage on the vertical axis. The diagram includes a straight diagonal line representing perfect income equality. Two countries, Country A and Country B, are plotted on this diagram. The curve representing Country A is positioned significantly farther away from the line of perfect equality than the curve for Country B. Based on this visual information, what is the most logical conclusion about the income inequality in these two countries?
Policy Impact on Income Distribution
On a standard income distribution diagram, if the area between the line of perfect equality and a country's Lorenz curve becomes smaller over time, this indicates that the country's Gini coefficient is increasing.
Calculating an Inequality Index from a Distribution Graph
The Relationship Between Lorenz Curve Geometry and Inequality Measurement
Formula for the Gini Coefficient Using Areas A and B
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Figure 2.4a: The Lorenz Curve and Gini Coefficient for Wealth Ownership
A country's income distribution is represented graphically. The area between the line of perfect equality and the curve representing the actual income distribution (defined as Area A) is calculated to be 0.18. The total triangular area under the line of perfect equality (defined as the sum of Area A and Area B) is 0.5. Based on these values, what is the Gini coefficient for this country?
Comparative Inequality Analysis
Analyzing Changes in Income Distribution
Consider a society's income distribution represented graphically. If a policy change causes the area between the line of perfect equality and the curve of actual distribution (Area A) to increase, while the area under the curve of actual distribution (Area B) remains constant, the calculated measure of income inequality will necessarily increase.